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Kirchhoff’s Law of Heat Radiation | Kirchhoff’s Law | What is Kirchhoff’s Law

Kirchhoff’s Law of Heat Radiation | Kirchhoff’s Law | What is Kirchhoff’s Law :- According to Kirchhoff’s law at a given temperature, for all bodies, the ratio of their spectral emissive power to their spectral absorptive power remains constant, and this constant is equal to the spectral emissive power of an ideal black body at the same temperature.

$\displaystyle \Rightarrow \frac{{{e}_{\lambda }}}{{{a}_{\lambda }}}=constant$

If E_λ and A_λ are the emissive power and absorptive power for a perfect black body, then using Kirchhoff’s law,

$\displaystyle \frac{{{e}_{\lambda }}}{{{a}_{\lambda }}}=\frac{{{E}_{\lambda }}}{{{A}_{\lambda }}}$

Since for a perfect black body A_λ = 1, so

$\displaystyle \frac{{{e}_{\lambda }}}{{{a}_{\lambda }}}={{E}_{\lambda }}$

Proof

Let a small amount of heat radiation be incident per second per unit area on a body within a narrow wavelength range , i.e., between (λ – ½) and (λ + ½).

Using the law of conservation of energy,

Heat Incident = Heat Reflected + Heat Emitted

$\displaystyle dQ=(dQ-{{a}_{\lambda }}dQ)+{{e}_{\lambda }}d\lambda$

$\displaystyle \Rightarrow {{e}_{\lambda }}d\lambda ={{a}_{\lambda }}dQ$ …..(1)

For a perfectly black body,

$\displaystyle {{e}_{\lambda }}={{E}_{\lambda }}$ and $\displaystyle {{a}_{\lambda }}=1$

$\displaystyle \Rightarrow {{E}_{\lambda }}d\lambda =(1).dQ$

$\displaystyle \Rightarrow dQ={{E}_{\lambda }}d\lambda$

Using the value of dQ in equation (1),

$\displaystyle {{e}_{\lambda }}d\lambda ={{a}_{\lambda }}({{E}_{\lambda }}d\lambda )$

$\displaystyle \Rightarrow \frac{{{e}_{\lambda }}}{{{a}_{\lambda }}}={{E}_{\lambda }}$

Applications of Kirchhoff’s Law of Heat Radiation

According to Kirchhoff’s Law, as the ratio of emissive power to the absorptive power of a body is a constant quantity, it means a body having greater emissive power must have greater absorptive power also, i.e., good absorbers are good emitters and bad absorbers are bad emitters. Here are some important and practical applications of Kirchhoff’s Law of Heat Radiation :

(1). Black Body Radiation Studies

Kirchhoff’s law laid the foundation for understanding black body radiation, which further led to Planck’s law, Stefan–Boltzmann law, and the quantum theory of radiation.

(2). Thermal Imaging and Infrared Devices

In thermal imaging and infrared sensing, objects with high emissivity emit more infrared radiation, making them easier to detect and visualize using thermal cameras and night vision devices.

(3). Design of Solar Absorbers and Heaters

Surfaces used in solar panels, solar cookers, and solar heaters are designed to be good absorbers and emitters, following Kirchhoff’s principle.

(4). Thermal Insulation and Coating

Surfaces meant to retain heat (like thermos flasks) are made of poor absorbers and poor emitters (e.g., shiny metallic surfaces) to reduce heat loss via radiation.

(5). Temperature Measurement (Pyrometry)

Optical pyrometers (A non-contact device that measures high temperatures by matching a filament’s brightness to that of a glowing object, ideal for molten metals, furnaces, and other extreme heat sources) measure temperature based on the emitted radiation from a hot body. The measurement relies on comparing the emitted radiation to that of a black body.

(6). Astronomy and Astrophysics

Kirchhoff’s law is used to analyze stellar radiation. By studying the emitted spectra of stars, scientists determine temperature, composition, and structure of celestial bodies.

(7). Heated Painted China

A piece of decorative china (e.g., a ceramic plate) is heated to a high temperature (about 1000°C) in a kiln or furnace. In a well-lit room, it may appear only slightly warm or not visibly glowing at all. But when it is taken into a dark room, it suddenly appears to glow visibly—often with a dull red or orange light.

(8). Fraunhofer Lines in Solar Spectrum

Fraunhofer lines are dark lines that appear in the spectrum of sunlight. The Sun’s core, called the photosphere, emits white light containing all colors. As this light passes outward through the Sun’s atmosphere, known as the chromosphere, certain gases there absorb specific wavelengths of light. This absorption removes those colors from the spectrum, creating dark lines—called Fraunhofer lines—in the observed solar spectrum.

During a total solar eclipse, the bright light from the photosphere is completely blocked by the Moon, so it doesn’t reach the Earth. Instead, only the light emitted by the chromosphere is visible. Because the chromosphere’s gases emit light at the same wavelengths they absorb, these Fraunhofer lines appear as bright lines in the solar spectrum observed at that moment.

This phenomenon beautifully demonstrates Kirchhoff’s law, which states that good absorbers of light at certain wavelengths are also good emitters at those wavelengths.

(9). In deserts, the days are hot and the nights are cold
The sand is rough and dark in color, so it absorbs sunlight well, making the days very hot. According to Kirchhoff’s Law, anything that is a good absorber is also a good emitter of heat. So at night, the sand gives off the heat quickly, making the nights cold.

Example 1.

Fraunhofer line of the solar system is an example of :

(A) line emission spectrum

(B) emission of band spectrum

(D) none of the above

Solution :

Fraunhofer lines are dark lines seen in the Sun’s spectrum. They were first noticed as dark gaps in the sunlight’s color pattern. Kirchhoff found that each element produces its own special set of lines. He realized that these dark lines appear because elements in the Sun’s upper layers absorb certain colors of light. So, Fraunhofer lines are an example of an absorption spectrum, hence option (C) is correct.

Kirchhoff’s Law of Heat Radiation | Kirchhoff’s Law | What is Kirchhoff’s Law

Applications of Kirchhoff’s Law of Heat Radiation

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